The action of the mapping class group on metrics of positive scalar curvature
- We present a rigidity theorem for the action of the mapping class group π0(Diff(M)) on the space R+(M) of metrics of positive scalar curvature for high dimensional manifolds M. This result is applicable to a great number of cases, for example to simply connected 6-manifolds and high dimensional spheres. Our proof is fairly direct, using results from parametrised Morse theory, the 2-index theorem and computations on certain metrics on the sphere. We also give a non-triviality criterion and a classification of the action for simply connected 7-dimensional Spin-manifolds.
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| Author: | Georg FrenckORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1049205 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/104920 |
| ISSN: | 0025-5831OPAC |
| ISSN: | 1432-1807OPAC |
| Parent Title (German): | Mathematische Annalen |
| Publisher: | Springer Science and Business Media LLC |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2022 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2023/06/16 |
| Tag: | General Mathematics |
| Volume: | 382 |
| Issue: | 3-4 |
| First Page: | 1143 |
| Last Page: | 1180 |
| DOI: | https://doi.org/10.1007/s00208-021-02235-1 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Differentialgeometrie | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |
